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Suppose you stand with one foot on ceramic flooring and one foot on a wool carpet, making contact over an area of $\text{80}\text{.}0\phantom{\rule{0.25em}{0ex}}{\text{cm}}^{2}$ with each foot. Both the ceramic and the carpet are 2.00 cm thick and are $\text{10.}\mathrm{0\xba}\text{C}$ on their bottom sides. At what rate must heat transfer occur from each foot to keep the top of the ceramic and carpet at $\text{33}\text{.}\mathrm{0\xba}\text{C}$ ?
A man consumes 3000 kcal of food in one day, converting most of it to maintain body temperature. If he loses half this energy by evaporating water (through breathing and sweating), how many kilograms of water evaporate?
2.59 kg
(a) A firewalker runs across a bed of hot coals without sustaining burns. Calculate the heat transferred by conduction into the sole of one foot of a firewalker given that the bottom of the foot is a 3.00-mm-thick callus with a conductivity at the low end of the range for wood and its density is $\text{300}{\text{kg/m}}^{3}$ . The area of contact is $\text{25}\text{.}0{\text{cm}}^{2}$ , the temperature of the coals is $\text{700\xba}\text{C}$ , and the time in contact is 1.00 s.
(b) What temperature increase is produced in the $\text{25}\text{.}0{\text{cm}}^{3}$ of tissue affected?
(c) What effect do you think this will have on the tissue, keeping in mind that a callus is made of dead cells?
(a) What is the rate of heat conduction through the 3.00-cm-thick fur of a large animal having a $1\text{.}{\text{40-m}}^{2}$ surface area? Assume that the animal’s skin temperature is $\text{32}\text{.}\mathrm{0\xba}\text{C}$ , that the air temperature is $-5\text{.}\text{00\xba}\text{C}$ , and that fur has the same thermal conductivity as air. (b) What food intake will the animal need in one day to replace this heat transfer?
(a) 39.7 W
(b) 820 kcal
A walrus transfers energy by conduction through its blubber at the rate of 150 W when immersed in $-1\text{.00\xbaC}$ water. The walrus’s internal core temperature is $\text{37.}\mathrm{0\xba}\text{C}$ , and it has a surface area of $2\text{.00}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{2}$ . What is the average thickness of its blubber, which has the conductivity of fatty tissues without blood?
Compare the rate of heat conduction through a 13.0-cm-thick wall that has an area of $\text{10}\text{.}0{\text{m}}^{2}$ and a thermal conductivity twice that of glass wool with the rate of heat conduction through a window that is 0.750 cm thick and that has an area of $2\text{.}\text{00}{\text{m}}^{2}$ , assuming the same temperature difference across each.
35 to 1, window to wall
Suppose a person is covered head to foot by wool clothing with average thickness of 2.00 cm and is transferring energy by conduction through the clothing at the rate of 50.0 W. What is the temperature difference across the clothing, given the surface area is $1\text{.}\text{40}{\text{m}}^{2}$ ?
Some stove tops are smooth ceramic for easy cleaning. If the ceramic is 0.600 cm thick and heat conduction occurs through the same area and at the same rate as computed in [link] , what is the temperature difference across it? Ceramic has the same thermal conductivity as glass and brick.
$1\text{.}\text{05}\times {\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{K}$
One easy way to reduce heating (and cooling) costs is to add extra insulation in the attic of a house. Suppose the house already had 15 cm of fiberglass insulation in the attic and in all the exterior surfaces. If you added an extra 8.0 cm of fiberglass to the attic, then by what percentage would the heating cost of the house drop? Take the single story house to be of dimensions 10 m by 15 m by 3.0 m. Ignore air infiltration and heat loss through windows and doors.
(a) Calculate the rate of heat conduction through a double-paned window that has a $1\text{.}\text{50}{\text{-m}}^{2}$ area and is made of two panes of 0.800-cm-thick glass separated by a 1.00-cm air gap. The inside surface temperature is $\text{15}\text{.}\mathrm{0\xba}\text{C}$ , while that on the outside is $-\text{10}\text{.}\mathrm{0\xba}\text{C}$ . (Hint: There are identical temperature drops across the two glass panes. First find these and then the temperature drop across the air gap. This problem ignores the increased heat transfer in the air gap due to convection.)
(b) Calculate the rate of heat conduction through a 1.60-cm-thick window of the same area and with the same temperatures. Compare your answer with that for part (a).
(a) 83 W
(b) 24 times that of a double pane window.
Many decisions are made on the basis of the payback period: the time it will take through savings to equal the capital cost of an investment. Acceptable payback times depend upon the business or philosophy one has. (For some industries, a payback period is as small as two years.) Suppose you wish to install the extra insulation in [link] . If energy cost $1.00 per million joules and the insulation was $4.00 per square meter, then calculate the simple payback time. Take the average $\text{\Delta}T$ for the 120 day heating season to be $\text{15.}\mathrm{0\xba}\text{C}$ .
For the human body, what is the rate of heat transfer by conduction through the body’s tissue with the following conditions: the tissue thickness is 3.00 cm, the change in temperature is $2\text{.}\text{00\xba}\text{C}$ , and the skin area is $1\text{.}\text{50}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{2}$ . How does this compare with the average heat transfer rate to the body resulting from an energy intake of about 2400 kcal per day? (No exercise is included.)
20.0 W, 17.2% of 2400 kcal per day
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